The experiment also revealed room for further improvements. Considering the discreteness of the musical notes, a reinforcement learning approach may be more suitable [1]}, making the prediction more sparse and replacing the peak-picking with trainable action.
The onset-enhancement on audio similarity is a function carefully-chosen in order to approximate \(L_y\)  when \(x\)  and \(\hat{x}\)  are given. Unfortunately, the approximation is limited because the exact drum sounds in \(x\)  are not given, and therefore a perfect reconstruct of (onsets of) the input audio (\(L_x(x, \hat{x})=0\) ) does not lead to a perfect transcription (\(L_y(y, \hat{y})=0\) ). An alternative way would be measuring a similarity on a (perceptual) representation domain instead of the audio, for example, by learning a loss using forward-backward consistency (also known as a cyclic loss [2]}) or known audio features.
Lastly, the current synthesizer module is limited to drums as it does not handle the duration of notes. A trainable synthesizer can be used to expand DrummerNet to other instruments [3]}, [4]}, eventually leading to an unsupervised universal transcription system combined with instrument recognition.
